Related papers: Floquet engineering of continuous-time quantum wal…
It is demonstrated that in gate-based quantum computing architectures quantum walk is a natural mathematical description of quantum gates. It originates from field-matter interaction driving the system, but is not attached to specific qubit…
Discrete quantum walks are periodically driven systems with discrete time evolution. In contrast to ordinary Floquet systems, no microscopic Hamiltonian exists, and the one-period time evolution is given directly by a series of unitary…
Controlling interactions is the key element for quantum engineering of many-body systems. Using time-periodic driving, a naturally given many-body Hamiltonian of a closed quantum system can be transformed into an effective target…
A Floquet systems is a periodically driven quantum system. It can be described by a Floquet operator. If this unitary operator has a gap in the spectrum, then one can define associated topological bulk invariants which can either only…
Quantum walks are powerful kernels in quantum computing protocols that possess strong capabilities in speeding up various simulation and optimisation tasks. One striking example is given by quantum walkers evolving on glued trees for their…
Floquet engineering, i.e. driving the system with periodic Hamiltonians, not only provides great flexibility in analog quantum simulation, but also supports phase structures of great richness. It has been proposed that Floquet systems can…
Discrete-time quantum walks (QWs) represent robust and versatile platforms for the controlled engineering of single particle quantum dynamics, and have attracted special attention due to their algorithmic applications in quantum information…
A continuous-time quantum walk on a dynamic graph evolves by Schr\"odinger's equation with a sequence of Hamiltonians encoding the edges of the graph. This process is universal for quantum computing, but in general, the dynamic graph that…
Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more…
Over the past few years, topological insulators have taken center stage in solid state physics. The desire to tune the topological invariants of the bulk and thus control the number of edge states has steered theorists and experimentalists…
Quantum walks provide a versatile framework for probing the structural and dynamical properties of complex systems ranging from biological networks to synthetic materials. However, their realization on current noisy pre-fault-tolerant…
Open quantum systems can display periodic dynamics at the classical level either due to external periodic modulations or to self-pulsing phenomena typically following a Hopf bifurcation. In both cases, the quantum fluctuations around…
Hermitian Hamiltonians with time-periodic coefficients can be analyzed via Floquet theory, and have been extensively used for engineering Floquet Hamiltonians in standard quantum simulators. Generalized to non-Hermitian Hamiltonians,…
We study the effect of random scattering in quantum walks on a finite graph and compare it with the effect of repeated measurements. To this end, a constructive approach is employed by introducing a localized and a delocalized basis for the…
This dissertation presents investigations on dynamics of discrete-time quantum walk and some of its applications. Quantum walks has been exploited as an useful tool for quantum algorithms in quantum computing. Beyond quantum computational…
Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the…
Quantum walks can reconstruct quantum algorithms for quantum computation, where the precise controls of quantum state transfers between arbitrary distant sites are required. Here, we investigate quantum walks using a periodically…
Classical random walk formalism shows a significant role across a wide range of applications. As its quantum counterpart, the quantum walk is proposed as an important theoretical model for quantum computing. By exploiting the quantum…
The theory of random walks on finite graphs is well developed with numerous applications. In quantum walks, the propagation is governed by quantum mechanical rules; generalizing random walks to the quantum setting. They have been…
In Floquet engineering, periodic driving is used to realize novel phases of matter which are inaccessible in thermal equilibrium. For this purpose, the Floquet theory provides us a recipe of obtaining a static effective Hamiltonian.…